# import netflix.txt
netflix <- read.delim("~/Desktop/MA611/data/netflix.txt")
#---Creating a time-series object---#
sales=netflix[,3]
data=ts(sales,start=c(2000,1),frequency = 4)
#---Plotting it----#
autoplot(data) + ggtitle("Netflix Quartly Sales from 2000 to 2009")
#---Checking seasonality through polar-plot---#
ggseasonplot(data, year.labels=FALSE, continuous=TRUE, polar = TRUE)+
ggtitle("Seasonality through polarmap for Netflix sales figures")
#---Checking seasonality through heatmap---#
Time.Stamp=seq(1,nrow(netflix),1)
data.modified=cbind(Time.Stamp,netflix)
ggplot(data.modified,aes(x = Time.Stamp, y = 1)) +
geom_tile(aes(fill = sales)) +
scale_fill_gradient2(low = "navy", mid = "yellow",
high = "red", midpoint=28) + ggtitle("Seasonality through heatmap for Netflix sales")+
ylab("") + scale_y_discrete(expand=c(0,0))
# Classic Decomposition
#---Decomposing it and plotting the decomposition----#
dec=decompose(data)
plot(decompose(data))
#--Checking the strength of trend and seasonality for Netflix data---#
# FT
ft <- 1-var(dec$random,na.rm=TRUE)/var((dec$trend+dec$random),na.rm=TRUE)
# FS
fs <- 1-var(dec$random,na.rm=TRUE)/var((dec$seasonal+dec$random),na.rm=TRUE)
data.frame(cbind(ft,fs))
## ft fs
## 1 0.9990173 0.3788519
#---Now doing an stl decomposition---#
decomp=stl(data,t.window = 5,s.window="periodic", robust=TRUE)
decomp
## Call:
## stl(x = data, s.window = "periodic", t.window = 5, robust = TRUE)
##
## Components
## seasonal trend remainder
## 2000 Q1 1.3157587 3.854241 0.000000e+00
## 2000 Q2 0.9304170 7.362308 -1.142725e+00
## 2000 Q3 -0.6903739 10.870374 0.000000e+00
## 2000 Q4 -1.5558018 13.307308 1.638494e+00
## 2001 Q1 1.3157587 15.744241 0.000000e+00
## 2001 Q2 0.9304170 17.657308 -2.277245e-01
## 2001 Q3 -0.6903739 19.570374 0.000000e+00
## 2001 Q4 -1.5558018 24.392308 -1.216506e+00
## 2002 Q1 1.3157587 29.214241 0.000000e+00
## 2002 Q2 0.9304170 35.317308 1.122755e-01
## 2002 Q3 -0.6903739 41.420374 0.000000e+00
## 2002 Q4 -1.5558018 47.887308 -1.141506e+00
## 2003 Q1 1.3157587 54.354241 0.000000e+00
## 2003 Q2 0.9304170 63.622308 -1.362725e+00
## 2003 Q3 -0.6903739 72.890374 0.000000e+00
## 2003 Q4 -1.5558018 85.697308 -2.951506e+00
## 2004 Q1 1.3157587 98.504241 3.126388e-13
## 2004 Q2 0.9304170 118.779583 1.421085e-13
## 2004 Q3 -0.6903739 130.497692 1.060268e+01
## 2004 Q4 -1.5558018 142.215802 0.000000e+00
## 2005 Q1 1.3157587 152.657692 -1.523451e+00
## 2005 Q2 0.9304170 163.099583 0.000000e+00
## 2005 Q3 -0.6903739 178.827692 -5.397319e+00
## 2005 Q4 -1.5558018 194.555802 0.000000e+00
## 2006 Q1 1.3157587 216.487692 6.326549e+00
## 2006 Q2 0.9304170 238.419583 0.000000e+00
## 2006 Q3 -0.6903739 258.602692 -1.962319e+00
## 2006 Q4 -1.5558018 278.785802 0.000000e+00
## 2007 Q1 1.3157587 290.772692 1.323155e+01
## 2007 Q2 0.9304170 302.759583 0.000000e+00
## 2007 Q3 -0.6903739 303.337692 -8.677319e+00
## 2007 Q4 -1.5558018 303.915802 0.000000e+00
## 2008 Q1 1.3157587 320.297692 4.566549e+00
## 2008 Q2 0.9304170 336.679583 0.000000e+00
## 2008 Q3 -0.6903739 349.087692 -7.127319e+00
## 2008 Q4 -1.5558018 361.495802 0.000000e+00
## 2009 Q1 1.3157587 384.577692 8.206549e+00
## 2009 Q2 0.9304170 407.659583 0.000000e+00
## 2009 Q3 -0.6903739 426.702692 -2.892319e+00
## 2009 Q4 -1.5558018 445.745802 1.477929e-12
#---Plotting the stl decomposition---#
autoplot(decomp)+
ggtitle("stl decomposition of Netflix data")
#---Now creating a lag-plot---#
gglagplot(data,lags=25,set.lags = 1:25)+
ggtitle("Lag plots, Netflix Sales")
#----Now creating an ACF plot---#
ggAcf(data,lag.max = 30)+ggtitle("ACF plot for Netflix sales data")
#---Now creating a tapered ACF plot---#
ggtaperedacf(data,lag.max=25,calc.ci = T,level=95,nsim = 100)+
ggtitle("Tapered ACF plot for Netflix sales data")
##################
#----Nomality checking-----#
##################
###################
###################
dec$random
## Qtr1 Qtr2 Qtr3 Qtr4
## 2000 NA NA 2.1181597 3.6124653
## 2001 -2.8598958 -1.4719792 0.6131597 0.5912153
## 2002 -3.1336458 -0.7769792 1.7819097 0.9174653
## 2003 -3.5436458 -2.2532292 1.0156597 -1.4062847
## 2004 -6.0211458 0.1130208 11.0781597 0.3812153
## 2005 -5.0636458 -1.8632292 -4.3780903 -1.3212847
## 2006 2.3388542 -1.1669792 -0.9668403 3.2937153
## 2007 10.9351042 3.6155208 -7.5755903 -4.8612847
## 2008 1.1526042 1.6767708 -6.0730903 -3.5937847
## 2009 3.8088542 -0.2594792 NA NA
# overestimating
gghistogram(dec$random)
## Warning: Removed 4 rows containing non-finite values (stat_bin).
ggAcf(dec$random,lag.max=20)
#---Naive modeling---#
fitted(naive(data))
## Qtr1 Qtr2 Qtr3 Qtr4
## 2000 NA 5.17 7.15 10.18
## 2001 13.39 17.06 18.36 18.88
## 2002 21.62 30.53 36.36 40.73
## 2003 45.19 55.67 63.19 72.20
## 2004 81.19 99.82 119.71 140.41
## 2005 140.66 152.45 164.03 172.74
## 2006 193.00 224.13 239.35 255.95
## 2007 277.23 305.32 303.69 293.97
## 2008 302.36 326.18 337.61 341.27
## 2009 359.94 394.10 408.59 423.12
#compare#
autoplot(data)+autolayer(fitted(naive(data)))+ggtitle("Tracking real and naively predicted Netflix sales")
## Warning: Removed 1 rows containing missing values (geom_path).
#--extract residuals--#
naive.model.resid=residuals(naive(data))
gghistogram(naive.model.resid) ## underestimating
## Warning: Removed 1 rows containing non-finite values (stat_bin).
ggAcf(naive.model.resid)
#--another way of extracting residuals---#
diff(sales)
## [1] 1.98 3.03 3.21 3.67 1.30 0.52 2.74 8.91 5.83 4.37 4.46 10.48
## [13] 7.52 9.01 8.99 18.63 19.89 20.70 0.25 11.79 11.58 8.71 20.26 31.13
## [25] 15.22 16.60 21.28 28.09 -1.63 -9.72 8.39 23.82 11.43 3.66 18.67 34.16
## [37] 14.49 14.53 21.07
#--checking normality---#
gghistogram(naive.model.resid)
## Warning: Removed 1 rows containing non-finite values (stat_bin).
ggAcf(naive.model.resid,lag.max=20)
autoplot(naive.model.resid)+ggtitle("Naive residuals showing reasonable stationarity")
netflix.ts <- data
#---State-space ETS modeling---#
########
intuitive.model=ets(netflix.ts,model="AAN")
intuitive.model
## ETS(A,A,N)
##
## Call:
## ets(y = netflix.ts, model = "AAN")
##
## Smoothing parameters:
## alpha = 0.9999
## beta = 0.1896
##
## Initial states:
## l = -0.1455
## b = 3.5045
##
## sigma: 9.3247
##
## AIC AICc BIC
## 331.9543 333.7190 340.3986
accuracy(intuitive.model)
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 1.749013 8.846204 5.942018 1.525494 5.891768 0.1309047 0.2066377
#autoplot(intuitive.model)
autoplot(fitted(intuitive.model))+autolayer(netflix.ts)+ggtitle("Comparing the intuitive ETS(AAN) fitted values to the actuals, Netflix")+ylab("Observed/Fitted")
forecast(intuitive.model,h=10)
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 2010 Q1 460.9564 449.0063 472.9065 442.6803 479.2325
## 2010 Q2 477.7233 459.1531 496.2935 449.3227 506.1239
## 2010 Q3 494.4902 469.6622 519.3182 456.5190 532.4614
## 2010 Q4 511.2571 480.1475 542.3667 463.6791 558.8352
## 2011 Q1 528.0240 490.4841 565.5640 470.6116 585.4364
## 2011 Q2 544.7909 500.6207 588.9612 477.2384 612.3435
## 2011 Q3 561.5579 510.5347 612.5811 483.5246 639.5911
## 2011 Q4 578.3248 520.2165 636.4331 489.4558 667.1937
## 2012 Q1 595.0917 529.6631 660.5203 495.0273 695.1561
## 2012 Q2 611.8586 538.8750 684.8422 500.2398 723.4774
autoplot(forecast(intuitive.model,h=10))+ggtitle("Extracting forecasts from the intuitive ETS(AAN), Netflix")+ylab("Values")
best.model=ets(netflix.ts)
best.model
## ETS(M,A,M)
##
## Call:
## ets(y = netflix.ts)
##
## Smoothing parameters:
## alpha = 0.9997
## beta = 0.84
## gamma = 1e-04
##
## Initial states:
## l = 2.2848
## b = 2.9875
## s = 0.9714 0.9843 1.0124 1.0319
##
## sigma: 0.062
##
## AIC AICc BIC
## 301.2328 307.2328 316.4327
accuracy(best.model)
## ME RMSE MAE MPE MAPE MASE
## Training set 0.6882066 6.837355 4.806047 0.5518281 3.945826 0.1058789
## ACF1
## Training set -0.1473851
#autoplot(best.model)
autoplot(fitted(best.model))+autolayer(netflix.ts)+ggtitle("Comparing the best ETS(MAM) fitted values to the actuals, Netflix")+ylab("Observed/Fitted")
forecast(best.model,h=10)
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 2010 Q1 499.8327 460.14173 539.5236 439.13062 560.5347
## 2010 Q2 517.7683 435.05494 600.4816 391.26913 644.2674
## 2010 Q3 530.0811 397.43001 662.7322 327.20875 732.9535
## 2010 Q4 549.4192 357.91313 740.9252 256.53595 842.3024
## 2011 Q1 611.6243 334.41903 888.8296 187.67541 1035.5732
## 2011 Q2 627.4393 273.94448 980.9341 86.81563 1168.0629
## 2011 Q3 636.7137 204.61719 1068.8101 -24.12087 1297.5482
## 2011 Q4 654.6498 131.70031 1177.5993 -145.13242 1454.4320
## 2012 Q1 723.4168 54.94848 1391.8851 -298.91727 1745.7509
## 2012 Q2 737.1111 -40.20095 1514.4232 -451.68510 1925.9073
autoplot(forecast(best.model,h=10))+ggtitle("Extracting forecasts from the best ETS(MAM), Netflix")+ylab("Values")
##########
##########
#---Comparing different models---#
##########
##########
illogical.model=ets(netflix.ts,model="ANN")
illogical.model
## ETS(A,N,N)
##
## Call:
## ets(y = netflix.ts, model = "ANN")
##
## Smoothing parameters:
## alpha = 0.9999
##
## Initial states:
## l = 5.2444
##
## sigma: 14.9002
##
## AIC AICc BIC
## 367.6136 368.2803 372.6802
accuracy(illogical.model)
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 10.97469 14.52295 11.54577 10.11385 10.37791 0.2543573 0.4209748
autoplot(fitted(illogical.model))+autolayer(netflix.ts)+ggtitle("Comparing the illogical ETS(ANN) fitted values to the actuals, Netflix")+ylab("Observed/Fitted")
naive.model=naive(netflix.ts)
naive.model
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 2010 Q1 444.19 425.3424 463.0376 415.3651 473.0149
## 2010 Q2 444.19 417.5354 470.8446 403.4254 484.9546
## 2010 Q3 444.19 411.5450 476.8350 394.2637 494.1163
## 2010 Q4 444.19 406.4948 481.8852 386.5401 501.8399
## 2011 Q1 444.19 402.0454 486.3346 379.7355 508.6445
## 2011 Q2 444.19 398.0230 490.3570 373.5836 514.7964
## 2011 Q3 444.19 394.3239 494.0561 367.9264 520.4536
## 2011 Q4 444.19 390.8809 497.4991 362.6607 525.7193
## 2012 Q1 444.19 387.6471 500.7329 357.7152 530.6648
## 2012 Q2 444.19 384.5886 503.7914 353.0375 535.3425
accuracy(naive.model)
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 11.25692 14.70688 11.83897 10.40919 10.60627 0.2608166 0.4067258
autoplot(fitted(naive.model))+autolayer(netflix.ts)+ggtitle("Comparing the naive fitted values to the actuals, Netflix")+ylab("Observed/Fitted")
forecast(naive.model,h=10)
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 2010 Q1 444.19 425.3424 463.0376 415.3651 473.0149
## 2010 Q2 444.19 417.5354 470.8446 403.4254 484.9546
## 2010 Q3 444.19 411.5450 476.8350 394.2637 494.1163
## 2010 Q4 444.19 406.4948 481.8852 386.5401 501.8399
## 2011 Q1 444.19 402.0454 486.3346 379.7355 508.6445
## 2011 Q2 444.19 398.0230 490.3570 373.5836 514.7964
## 2011 Q3 444.19 394.3239 494.0561 367.9264 520.4536
## 2011 Q4 444.19 390.8809 497.4991 362.6607 525.7193
## 2012 Q1 444.19 387.6471 500.7329 357.7152 530.6648
## 2012 Q2 444.19 384.5886 503.7914 353.0375 535.3425
autoplot(forecast(naive.model,h=10))+ggtitle("Extracting forecasts from the naive model, Netflix")+ylab("Values")
stl.randomwalk.model=stl(netflix.ts,t.window = 5,s.window="periodic", robust=TRUE)
stl.randomwalk.model
## Call:
## stl(x = netflix.ts, s.window = "periodic", t.window = 5, robust = TRUE)
##
## Components
## seasonal trend remainder
## 2000 Q1 1.3157587 3.854241 0.000000e+00
## 2000 Q2 0.9304170 7.362308 -1.142725e+00
## 2000 Q3 -0.6903739 10.870374 0.000000e+00
## 2000 Q4 -1.5558018 13.307308 1.638494e+00
## 2001 Q1 1.3157587 15.744241 0.000000e+00
## 2001 Q2 0.9304170 17.657308 -2.277245e-01
## 2001 Q3 -0.6903739 19.570374 0.000000e+00
## 2001 Q4 -1.5558018 24.392308 -1.216506e+00
## 2002 Q1 1.3157587 29.214241 0.000000e+00
## 2002 Q2 0.9304170 35.317308 1.122755e-01
## 2002 Q3 -0.6903739 41.420374 0.000000e+00
## 2002 Q4 -1.5558018 47.887308 -1.141506e+00
## 2003 Q1 1.3157587 54.354241 0.000000e+00
## 2003 Q2 0.9304170 63.622308 -1.362725e+00
## 2003 Q3 -0.6903739 72.890374 0.000000e+00
## 2003 Q4 -1.5558018 85.697308 -2.951506e+00
## 2004 Q1 1.3157587 98.504241 3.126388e-13
## 2004 Q2 0.9304170 118.779583 1.421085e-13
## 2004 Q3 -0.6903739 130.497692 1.060268e+01
## 2004 Q4 -1.5558018 142.215802 0.000000e+00
## 2005 Q1 1.3157587 152.657692 -1.523451e+00
## 2005 Q2 0.9304170 163.099583 0.000000e+00
## 2005 Q3 -0.6903739 178.827692 -5.397319e+00
## 2005 Q4 -1.5558018 194.555802 0.000000e+00
## 2006 Q1 1.3157587 216.487692 6.326549e+00
## 2006 Q2 0.9304170 238.419583 0.000000e+00
## 2006 Q3 -0.6903739 258.602692 -1.962319e+00
## 2006 Q4 -1.5558018 278.785802 0.000000e+00
## 2007 Q1 1.3157587 290.772692 1.323155e+01
## 2007 Q2 0.9304170 302.759583 0.000000e+00
## 2007 Q3 -0.6903739 303.337692 -8.677319e+00
## 2007 Q4 -1.5558018 303.915802 0.000000e+00
## 2008 Q1 1.3157587 320.297692 4.566549e+00
## 2008 Q2 0.9304170 336.679583 0.000000e+00
## 2008 Q3 -0.6903739 349.087692 -7.127319e+00
## 2008 Q4 -1.5558018 361.495802 0.000000e+00
## 2009 Q1 1.3157587 384.577692 8.206549e+00
## 2009 Q2 0.9304170 407.659583 0.000000e+00
## 2009 Q3 -0.6903739 426.702692 -2.892319e+00
## 2009 Q4 -1.5558018 445.745802 1.477929e-12
stl.forecast=forecast(stl.randomwalk.model, h=10,method="naive",robust=FALSE)
stl.randomwalk.model$time.series[,1]+stl.randomwalk.model$time.series[,2]
## Qtr1 Qtr2 Qtr3 Qtr4
## 2000 5.170000 8.292725 10.180000 11.751506
## 2001 17.060000 18.587725 18.880000 22.836506
## 2002 30.530000 36.247725 40.730000 46.331506
## 2003 55.670000 64.552725 72.200000 84.141506
## 2004 99.820000 119.710000 129.807319 140.660000
## 2005 153.973451 164.030000 178.137319 193.000000
## 2006 217.803451 239.350000 257.912319 277.230000
## 2007 292.088451 303.690000 302.647319 302.360000
## 2008 321.613451 337.610000 348.397319 359.940000
## 2009 385.893451 408.590000 426.012319 444.190000
autoplot(stl.randomwalk.model$time.series[,1]+stl.randomwalk.model$time.series[,2])+autolayer(netflix.ts)+ggtitle("Comparing the stl signal values to the actuals, Netflix")+ylab("Observed/stl.Signal")
autoplot(stl.forecast)+ggtitle("Extracting forecasts from the stl model, Netflix")+ylab("Values")
accuracy(stl.forecast)
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 11.33055 14.36951 11.80973 10.93826 11.10056 0.2601723 0.4861571
###################
#---Checking residual assumptions------#
###################
checkresiduals(forecast(naive.model))
##
## Ljung-Box test
##
## data: Residuals from Naive method
## Q* = 19.518, df = 8, p-value = 0.01232
##
## Model df: 0. Total lags used: 8
checkresiduals(forecast(illogical.model))
##
## Ljung-Box test
##
## data: Residuals from ETS(A,N,N)
## Q* = 20.246, df = 6, p-value = 0.002504
##
## Model df: 2. Total lags used: 8
checkresiduals(forecast(intuitive.model))
##
## Ljung-Box test
##
## data: Residuals from ETS(A,A,N)
## Q* = 28.556, df = 4, p-value = 9.62e-06
##
## Model df: 4. Total lags used: 8
checkresiduals(forecast(best.model))
##
## Ljung-Box test
##
## data: Residuals from ETS(M,A,M)
## Q* = 31.454, df = 3, p-value = 6.82e-07
##
## Model df: 8. Total lags used: 11
###############
#--Forced damping--#
###############
damped.model=ets(netflix.ts,model="AAN",damped = TRUE)
damped.model
## ETS(A,Ad,N)
##
## Call:
## ets(y = netflix.ts, model = "AAN", damped = TRUE)
##
## Smoothing parameters:
## alpha = 0.9999
## beta = 0.2737
## phi = 0.9799
##
## Initial states:
## l = 4.6853
## b = 1.5605
##
## sigma: 9.5868
##
## AIC AICc BIC
## 335.0446 337.5900 345.1779
accuracy(damped.model)
## ME RMSE MAE MPE MAPE MASE ACF1
## Training set 2.074655 8.967594 6.024618 2.425019 5.713945 0.1327244 0.1601022
forecast(damped.model,h=100)
## Point Forecast Lo 80 Hi 80 Lo 95 Hi 95
## 2010 Q1 460.8196 448.53371 473.1056 442.029935 479.6093
## 2010 Q2 477.1161 457.27494 496.9572 446.771673 507.4605
## 2010 Q3 493.0855 465.74624 520.4247 451.273730 534.8972
## 2010 Q4 508.7344 473.65972 543.8090 455.092327 562.3764
## 2011 Q1 524.0692 480.95426 567.1841 458.130605 590.0077
## 2011 Q2 539.0962 487.62629 590.5662 460.379751 617.8127
## 2011 Q3 553.8217 493.69122 613.9522 461.860065 645.7833
## 2011 Q4 568.2516 499.17112 637.3322 462.602104 673.9012
## 2012 Q1 582.3920 504.09007 660.6939 462.639547 702.1444
## 2012 Q2 596.2485 508.47222 684.0248 462.006260 730.4908
## 2012 Q3 609.8270 512.34100 707.3129 460.735048 758.9189
## 2012 Q4 623.1329 515.71877 730.5470 458.857159 787.4087
## 2013 Q1 636.1718 518.62672 753.7169 456.402115 815.9415
## 2013 Q2 648.9490 521.08489 776.8131 453.397720 844.5003
## 2013 Q3 661.4698 523.11220 799.8274 449.870121 873.0694
## 2013 Q4 673.7393 524.72651 822.7520 445.843913 901.6346
## 2014 Q1 685.7625 525.94469 845.5803 441.342247 930.1828
## 2014 Q2 697.5445 526.78274 868.3062 436.386941 958.7020
## 2014 Q3 709.0899 527.25578 890.9241 430.998580 987.1813
## 2014 Q4 720.4037 527.37817 913.4293 425.196618 1015.6108
## 2015 Q1 731.4904 527.16357 935.8173 418.999459 1043.9814
## 2015 Q2 742.3546 526.62494 958.0843 412.424541 1072.2847
## 2015 Q3 753.0008 525.77466 980.2269 405.488407 1100.5132
## 2015 Q4 763.4333 524.62451 1002.2421 398.206769 1128.6598
## 2016 Q1 773.6564 523.18574 1024.1271 390.594569 1156.7183
## 2016 Q2 783.6744 521.46912 1045.8797 382.666031 1184.6827
## 2016 Q3 793.4913 519.48492 1067.4977 374.434708 1212.5479
## 2016 Q4 803.1112 517.24299 1088.9793 365.913528 1240.3088
## 2017 Q1 812.5380 514.75279 1110.3232 357.114833 1267.9611
## 2017 Q2 821.7756 512.02335 1131.5278 348.050416 1295.5008
## 2017 Q3 830.8278 509.06336 1152.5923 338.731553 1322.9241
## 2017 Q4 839.6984 505.88118 1173.5156 329.169033 1350.2277
## 2018 Q1 848.3909 502.48481 1194.2970 319.373189 1377.4086
## 2018 Q2 856.9090 498.88196 1214.9359 309.353921 1404.4640
## 2018 Q3 865.2561 495.08006 1235.4321 299.120719 1431.3914
## 2018 Q4 873.4357 491.08624 1255.7851 288.682687 1458.1886
## 2019 Q1 881.4511 486.90739 1275.9948 278.048565 1484.8536
## 2019 Q2 889.3057 482.55012 1296.0612 267.226742 1511.3846
## 2019 Q3 897.0026 478.02082 1315.9843 256.225278 1537.7799
## 2019 Q4 904.5450 473.32566 1335.7644 245.051920 1564.0381
## 2020 Q1 911.9361 468.47059 1355.4016 233.714116 1590.1581
## 2020 Q2 919.1789 463.46132 1374.8964 222.219028 1616.1387
## 2020 Q3 926.2762 458.30340 1394.2491 210.573549 1641.9789
## 2020 Q4 933.2312 453.00219 1413.4602 198.784312 1667.6781
## 2021 Q1 940.0465 447.56283 1432.5303 186.857704 1693.2354
## 2021 Q2 946.7251 441.99033 1451.4599 174.799873 1718.6504
## 2021 Q3 953.2697 436.28951 1470.2498 162.616745 1743.9226
## 2021 Q4 959.6829 430.46503 1488.9007 150.314027 1769.0517
## 2022 Q1 965.9674 424.52140 1507.4133 137.897222 1794.0375
## 2022 Q2 972.1257 418.46298 1525.7884 125.371631 1818.8798
## 2022 Q3 978.1605 412.29399 1544.0270 112.742369 1843.5786
## 2022 Q4 984.0741 406.01852 1562.1297 100.014366 1868.1339
## 2023 Q1 989.8691 399.64051 1580.0977 87.192378 1892.5458
## 2023 Q2 995.5478 393.16380 1597.9317 74.280993 1916.8145
## 2023 Q3 1001.1125 386.59208 1615.6328 61.284638 1940.9403
## 2023 Q4 1006.5655 379.92893 1633.2020 48.207584 1964.9234
## 2024 Q1 1011.9090 373.17783 1650.6403 35.053954 1988.7641
## 2024 Q2 1017.1454 366.34215 1667.9486 21.827728 2012.4630
## 2024 Q3 1022.2766 359.42513 1685.1281 8.532746 2036.0205
## 2024 Q4 1027.3049 352.42993 1702.1798 -4.827282 2059.4370
## 2025 Q1 1032.2322 345.35962 1719.1048 -18.248777 2082.7132
## 2025 Q2 1037.0607 338.21714 1735.9042 -31.728280 2105.8496
## 2025 Q3 1041.7922 331.00538 1752.5791 -45.262452 2128.8469
## 2025 Q4 1046.4288 323.72711 1769.1305 -58.848070 2151.7057
## 2026 Q1 1050.9724 316.38502 1785.5597 -72.482019 2174.4267
## 2026 Q2 1055.4247 308.98174 1801.8677 -86.161290 2197.0107
## 2026 Q3 1059.7877 301.51980 1818.0556 -99.882979 2219.4584
## 2026 Q4 1064.0631 294.00164 1834.1246 -113.644279 2241.7705
## 2027 Q1 1068.2527 286.42966 1850.0758 -127.442479 2263.9480
## 2027 Q2 1072.3583 278.80616 1865.9104 -141.274960 2285.9915
## 2027 Q3 1076.3814 271.13338 1881.6295 -155.139194 2307.9021
## 2027 Q4 1080.3238 263.41348 1897.2342 -169.032736 2329.6804
## 2028 Q1 1084.1871 255.64858 1912.7256 -182.953225 2351.3274
## 2028 Q2 1087.9729 247.84071 1928.1050 -196.898381 2372.8441
## 2028 Q3 1091.6826 239.99185 1943.3734 -210.866002 2394.2312
## 2028 Q4 1095.3179 232.10393 1958.5319 -224.853960 2415.4898
## 2029 Q1 1098.8803 224.17880 1973.5818 -238.860199 2436.6208
## 2029 Q2 1102.3711 216.21826 1988.5240 -252.882734 2457.6250
## 2029 Q3 1105.7919 208.22408 2003.3598 -266.919648 2478.5035
## 2029 Q4 1109.1441 200.19794 2018.0902 -280.969087 2499.2573
## 2030 Q1 1112.4290 192.14149 2032.7164 -295.029264 2519.8872
## 2030 Q2 1115.6479 184.05633 2047.2395 -309.098452 2540.3943
## 2030 Q3 1118.8022 175.94401 2061.6605 -323.174982 2560.7795
## 2030 Q4 1121.8933 167.80603 2075.9805 -337.257243 2581.0438
## 2031 Q1 1124.9223 159.64385 2090.2007 -351.343681 2601.1882
## 2031 Q2 1127.8905 151.45888 2104.3221 -365.432793 2621.2138
## 2031 Q3 1130.7991 143.25248 2118.3458 -379.523132 2641.1214
## 2031 Q4 1133.6494 135.02599 2132.2728 -393.613298 2660.9121
## 2032 Q1 1136.4424 126.78070 2146.1042 -407.701940 2680.5868
## 2032 Q2 1139.1794 118.51785 2159.8410 -421.787756 2700.1466
## 2032 Q3 1141.8615 110.23866 2173.4844 -435.869490 2719.5925
## 2032 Q4 1144.4898 101.94430 2187.0352 -449.945927 2738.9254
## 2033 Q1 1147.0653 93.63591 2200.4946 -464.015898 2758.1464
## 2033 Q2 1149.5891 85.31460 2213.8635 -478.078275 2777.2564
## 2033 Q3 1152.0622 76.98143 2227.1430 -492.131970 2796.2564
## 2033 Q4 1154.4857 68.63744 2240.3341 -506.175933 2815.1474
## 2034 Q1 1156.8606 60.28364 2253.4376 -520.209153 2833.9304
## 2034 Q2 1159.1878 51.92100 2266.4547 -534.230657 2852.6064
## 2034 Q3 1161.4684 43.55048 2279.3862 -548.239503 2871.1762
## 2034 Q4 1163.7031 35.17298 2292.2332 -562.234788 2889.6410
autoplot(forecast(damped.model,h=100))+ggtitle("Extracting forecasts from trend-damped AAN, Netflix")
checkresiduals(damped.model)
##
## Ljung-Box test
##
## data: Residuals from ETS(A,Ad,N)
## Q* = 31.608, df = 3, p-value = 6.33e-07
##
## Model df: 5. Total lags used: 8
##############
##############
##############
################
#---On simulations---#
################
simulate(intuitive.model)
## Qtr1 Qtr2 Qtr3 Qtr4
## 2010 483.7831 513.3689 528.2873 553.9979
## 2011 575.1888 592.3600 608.9938 646.9377
## 2012 668.4516 707.5872 741.1059 769.0410
## 2013 800.5554 838.7958 880.4491 918.6317
## 2014 950.1046 969.6539 1008.1170 1038.3941
## 2015 1069.0269 1108.6436 1117.9986 1150.9169
## 2016 1191.8962 1233.6088 1274.5044 1314.2884
## 2017 1365.2982 1409.7686 1454.3235 1493.7692
## 2018 1532.4007 1582.7033 1666.0219 1711.8642
## 2019 1758.1163 1805.5605 1855.5084 1903.8551
autoplot(netflix.ts)+
autolayer(simulate(illogical.model,future=F),series = "simANN1")+
autolayer(simulate(illogical.model,future=F),series = "simANN2")+
autolayer(simulate(damped.model,future=F),series = "simdamped1")+
autolayer(simulate(damped.model,future=F),series = "simdamped2")+ylab("Real and simulated values")+
ggtitle("Simulating the past, Netflix")
autoplot(netflix.ts)+
autolayer(simulate(illogical.model,future=T),series = "simANN1")+
autolayer(simulate(illogical.model,future=T),series = "simANN2")+
autolayer(simulate(damped.model,future=T),series = "simdamped1")+
autolayer(simulate(damped.model,future=T),series = "simdamped2")+ylab("Real and simulated values")+
ggtitle("Simulating the future, Netflix")
######
#####
MAM1=simulate(best.model,future=F)
MAM2=simulate(best.model,future=F)
MAM3=simulate(best.model,future=F)
MAM4=simulate(best.model,future=F)
AAN1=simulate(intuitive.model,future=F)
AAN2=simulate(intuitive.model,future=F)
AAN3=simulate(intuitive.model,future=F)
AAN4=simulate(intuitive.model,future=F)
ANN1=simulate(illogical.model,future=F)
ANN2=simulate(illogical.model,future=F)
ANN3=simulate(illogical.model,future=F)
ANN4=simulate(illogical.model,future=F)
#Naive1=simulate(naive.model,future=F)
#Naive2=simulate(naive.model,future=F)
#Naive3=simulate(naive.model,future=F)
#Naive4=simulate(naive.model,future=F)
data=ts(cbind(MAM1,MAM2,MAM3,MAM4,AAN1,AAN2,AAN3,AAN4,ANN1,ANN2,ANN3,ANN4,netflix.ts),start=c(2000,1),frequency = 4)
dissimilarity=diss(data,METHOD="COR")
dissimilarity
## MAM1 MAM2 MAM3 MAM4 AAN1 AAN2
## MAM2 0.6151954
## MAM3 1.9673322 1.8937494
## MAM4 0.6765662 1.1148670 1.8872012
## AAN1 1.9188661 1.8390623 0.4759949 1.8092863
## AAN2 1.8748312 1.9462609 0.6311500 1.6014022 0.6472225
## AAN3 1.8994251 1.7473616 0.5474444 1.8801718 0.3000228 0.8747049
## AAN4 1.9528903 1.9165466 0.4119907 1.7671558 0.3131599 0.4190454
## ANN1 1.5827130 1.2199543 1.2788737 1.7413233 1.1375033 1.5457544
## ANN2 0.9274408 1.0357490 1.8183985 1.1382533 1.8355100 1.8030943
## ANN3 1.1177687 1.4164630 1.6928040 0.9588245 1.7725410 1.4929428
## ANN4 0.5351675 0.7203757 1.9533664 0.8419682 1.9920761 1.9051435
## netflix.ts 1.9473603 1.9515145 0.4231992 1.7337572 0.4296210 0.3115663
## AAN3 AAN4 ANN1 ANN2 ANN3 ANN4
## MAM2
## MAM3
## MAM4
## AAN1
## AAN2
## AAN3
## AAN4 0.5481173
## ANN1 0.9916845 1.2972458
## ANN2 1.8125665 1.8340317 1.5153817
## ANN3 1.8210869 1.6702093 1.8602124 1.0663360
## ANN4 1.9667951 1.9765064 1.5989999 0.8151843 1.0100359
## netflix.ts 0.6609106 0.1771690 1.3879294 1.8288415 1.6104559 1.9613553
hc.dpred <- hclust(dissimilarity)
plot(hc.dpred,main="Cluster dendogram, Netflix, Correlation distance")
